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Vectors and Derivatives (Product Rule): MATH 171 Problems 1-3 thumbnail

Vectors and Derivatives (Product Rule): MATH 171 Problems 1-3

Proving facts about the derivatives of vector functions including the product rule

CosineDerivativeDifference QuotientDot ProductGraphLimitLimit Definition of the DerivativeOrthogonalProduct RuleSineSum RuleTrigonometryVectorVector DerivativeVector Function
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Inverse Trigonometric Functions: MATH 171 Problems 4-6 thumbnail

Inverse Trigonometric Functions: MATH 171 Problems 4-6

Properties of inverse trig functions and the derivative of arctangent

AngleArccosineArcsineArctangentCodomainCosineDerivativeDifferentiationDomainGraphInverse FunctionInverse TrigonometryOne-to-oneSecantSineTangentTrigonometry
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Continuity: MATH 171 Problems 6 & 7 thumbnail

Continuity: MATH 171 Problems 6 & 7

Proving a piecewise function and a polynomial are continuous

ContinuousContinuous at x=aDiscontinuityDiscontinuous FunctionGraphLimitLimit PropertiesPiecewise FunctionPolynomialRational Function
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Derivatives and Rates of Change: MATH 171 Problems 1-3 thumbnail

Derivatives and Rates of Change: MATH 171 Problems 1-3

Using the limit definition to find derivatives of functions and vector functions

DerivativeDifference QuotientGraphLimitLimit Definition of the DerivativeLineRational FunctionSlopeSquare RootTangent LineVectorVector DerivativeVector Function
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Absolute Extrema: MATH 171 Problems 4 & 5 thumbnail

Absolute Extrema: MATH 171 Problems 4 & 5

Proving Fermat's Theorem and graphing local and absolute extrema

Absolute MaximumAbsolute MinimumCritical ValueDerivativeDifference QuotientDiscontinuous FunctionExtreme Value TheoremLimitLimit from the LeftLocal MaximumLocal MinimumOne-Sided LimitRelative MaximumRelative Minimum
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Studying the Shape of Curves: MATH 171 Problems 1-3 thumbnail

Studying the Shape of Curves: MATH 171 Problems 1-3

What the derivatives of a function tell us about the shape of its graph

Concave DownConcave UpDecreasingDecreasing FunctionDerivativeDiscontinuous FunctionFirst DerivativeGraphGraph of DerivativeIncreasingIncreasing FunctionLineRelative MaximumRelative MinimumSecond Derivative
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L'Hospital's Rule: MATH 171 Problems 7-9 thumbnail

L'Hospital's Rule: MATH 171 Problems 7-9

Proving L'Hospital's Rule and using it to evaluate limits

Chain RuleContinuousContinuous at x=aDerivativeDifferentiableeGraphIndeterminate FormL'Hopital's RuleLimitLimit Involving InfinityLogarithm
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Optimization: MATH 171 Problems 1-3 thumbnail

Optimization: MATH 171 Problems 1-3

Optimizing values in word problems

Absolute MaximumAbsolute MinimumAreaCritical ValueDerivativeDistance from a Point to a LineFirst Derivative TestGraphIncreasing FunctionLineMaximizeMinimizeRelative MaximumRelative MinimumSecond Derivative TestVolumeWord Problems
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Fundamental Theorem of Calculus: MATH 171 Problems 1-3 thumbnail

Fundamental Theorem of Calculus: MATH 171 Problems 1-3

Proving and then applying the Fundamental Theorem of Calculus

AntiderivativeAntiderivative of a FunctionConcave DownConcave UpContinuousDerivativeDifference QuotientDifferentiableExtreme Value TheoremFundamental Theorem of CalculusGraphGraph of AntiderivativeGraph of DerivativeIncreasingIntegralLimitSqueeze (or Sandwich) Theorem
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